Simplify the following expression: $ p = \dfrac{3}{7} + \dfrac{k - 8}{-6} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-6}{-6}$ $ \dfrac{3}{7} \times \dfrac{-6}{-6} = \dfrac{-18}{-42} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{k - 8}{-6} \times \dfrac{7}{7} = \dfrac{7k - 56}{-42} $ Therefore $ p = \dfrac{-18}{-42} + \dfrac{7k - 56}{-42} $ Now the expressions have the same denominator we can simply add the numerators: $p = \dfrac{-18 + 7k - 56}{-42} $ $p = \dfrac{7k - 74}{-42}$ Simplify the expression by dividing the numerator and denominator by -1: $p = \dfrac{-7k + 74}{42}$